I often play the higher-lower game with my students. I randomly generate a number 1 to 1000 and give a student 10 guesses. After each guess I tell them whether the number is higher or lower. With good mental math skills a student should always win.

This is a new variant:
I pick two numbers from 1 to 1000 and create an ordered pair. The student guesses coordinates and I tell them both (east/west/neither) and (north/south/neither).

How many guesses should I give?